Last month, David Fincher chose to play it coy when Entertainment Weekly asked about his latest film's Oscar chances. "There's too much anal rape in this movie to get nominated," he said. "I think we're very safe." But he's not safe in the slightest. The Girl With The Dragon Tattoo, his adaptation of Stieg Larsson's wildly successful novel (55m copies of the trilogy sold to date), is an exquisite work of art, regardless of some of its brutal content. "There was never any pressure from the studio to lighten it up," says the film's screenwriter, Steven Zaillian. "They understood that part of the reason the book is so successful is because it doesn't tiptoe around those issues."

Indeed, the studio, Sony, went further, embracing the problematic content and telling Fincher to build an adult franchise. Zaillian in turn was given carte blanche to go for it, with virtually no briefing. "There was really very little discussion, he recalls. It was, 'Read the book, see what you think.' And, 'We're not interested in setting it in the United States, we want to go to Sweden [where the novel is set].' That was basically the whole conversation."

As one of Hollywood's screenwriting elite, Zaillian, 58, has written for Spielberg (Schindler's List), Scorsese (Gangs Of New York), and Ridley Scott (Hannibal, American Gangster). His films often involve outcasts solving puzzles – Clarice Starling in Hannibal, Billy Beane in Moneyball, Ethan Hunt in Mission: Impossible – and The Girl With The Dragon Tattoo is no exception. At its heart is the relationship between disgraced magazine publisher Mikael Blomkvist (Daniel Craig) and the damaged, socially inept Lisbeth Salander (Rooney Mara), the hacker he hires to help crack the case of Harriet Vanger, who disappeared from her family's foreboding island in the mid-60s. As with Fincher's 2007 film Zodiac, it focuses heavily on the nuances of their investigation.

"I'm really interested in the process of anything," Zaillian says. "Follow the money, follow the story, follow the lies, whatever it is. This story has all of that. I love learning about things that way."

'I didn't change anything just for the sake of changing it. There's a lot right about the book, but one part, I thought we could do it a different way, and it could be a nice surprise'

Daniel Craig

He hopes Dragon Tattoo audiences will enjoy learning too – at least those who aren't familiar with Larsson's novel, let alone its two sequels or the Swedish film trilogy. For those who are, there will still be some surprises; one of the book's major plot points has been substantially changed. So how much was his writing governed by the novel's legacy?

"Not a lot," shrugs Zaillian. "I would say there is a kind of low-grade anxiety all the time, but I was never doing anything specifically to please or displease. I was simply trying to tell the story the best way I could, and push that out of my mind. I didn't change anything just for the sake of changing it. There's a lot right about the book, but that part, I thought we could do it a different way, and it could be a nice surprise for the people that have read it."

Sony is banking on the majority of the film's audience being Dragon Tattoo virgins. As successful and acclaimed as the Swedish film was in the States, it was still relatively minor. Says Zaillian: "People who would go to an arthouse cinema and watch a Swedish movie and read subtitles … it's a small percentage." David Fincher's film is tougher, sadder and a whole lot more beautiful than the Swedish one. It's also more complex, which may surprise at least those who were opposed to it when it was announced.

"I know we are playing into the European, and certainly the Swedish, predisposition that this is just a gigantic, monetary land grab," Fincher said recently in an interview with the Fincher Fanatic website.

Indeed, the most vocal critic was the original director, Niels Arden Oplev. "Even in Hollywood," he told the Word & Film website last year, "there seems to be a kind of anger about the remake, like, 'Why would they remake something when they can just go see the original?' Everybody who loves film will go see the original one. It's like: what do you want to see, the French version of La Femme Nikita or the American one?"

The Guardian reads these comments to Zaillian, who hasn't heard them, and he responds by saying that by the time his projects are officially announced and statements like that are made, he's usually already finished the job. "There's a lag time, so I didn't have to work with that," he says. "But I don't like the idea of remaking things, it's not something that I look to do. I've only done it once before, with All The King's Men [which he also directed], and it didn't turn out so well! It was the same thing: people attacked it for being not the original. So I get it, and it's not something that I look for, and that's the reason I didn't see the Swedish film. I didn't want to remake it."

'I imagined someone who could move through the streets of Stockholm almost invisibly even though she looks the way she looks … it's almost like a forcefield'

Rooney Mara. Photograph: Merrick Morton

Zaillian and Fincher spent a lot of time discussing the themes of Larsson's novels and how best to communicate them. This took them into some dark places, such as the psychological difference between rapists and serial killers, for example. A particular line of dialogue, which has one of the film's more deplorable characters psychologically bribing Salander, sums up that difference incredibly succinctly.

"We were talking about the main difference between the two, and this is really David, he's an expert on the subject," Zaillian half-jokes, in reference to the director's previous serial killer studies, Seven and Zodiac. "A rapist, or at least our rapist, is about exercising his power over somebody. A serial killer is about destruction; they get off on destroying something. It's not about having power over something, it's about eliminating it. What thrills them is slightly different."

Such diligent psychological exploration is also naturally afforded to Salander, and Rooney Mara's stunning performance elevates the character – already iconic – into cinema's hall of fame. Here, she's fantastically multi-layered, more aggressive than before, with a constant underlying rage, while also more feminine and in some ways more vulnerable. She looks and seems like an alien.

"I always imagined that she's someone who could move through the streets of Stockholm almost invisibly," says Zaillian, "even though she looks the way she looks, because of the way she dresses and the way she behaves. And it's not by design, I don't think. It's almost like a forcefield: 'Stay away from me.' She has no social graces. She has more experience with the dark side of human nature than the rest of us, but she has very little experience with the normal interaction between civilised people. And she just doesn't know how to behave."

Fincher has yet to sign up for a sequel – the public will be the judge of that, he joked at a Bafta Q&A last Sunday – although Sony is forging ahead, with Craig and Mara contracted for a new trilogy. Zaillian, meanwhile, is currently in the middle of the second screenplay.

"OK!" he laughs when I ask how it's going, not wanting to discuss it right now. "I hate everything until I'm deeper into it. It's going fine." On the basis of The Girl With The Dragon Tattoo, I'm inclined to believe him.

• This article was amended on 23 December 2011. The credit list in the above box included people who worked on the Swedish adaptation of The Girl With the Dragon Tattoo. This has been corrected.